1. To make the brownie, preheat oven to 350°F (176°C). Grease a 9×13 inch baking pan.
2. Combine the butter, sugar, vanilla extract and Baileys in a medium sized bowl. Add eggs and mix until well combined.
3. Combine flour, cocoa, baking powder and salt in another medium sized bowl, then slowly add dry ingredients to the egg mixture until well combined.
4. Pour the batter into the pan and spread evenly. Bake for 22-26 minutes, or until a toothpick comes out with a few moist crumbs.
5. While the brownie cools, make the chocolate mousse. Combine the egg yolks, sugar and Baileys in the top of a double boiler until combined. If you don’t have a double boiler, you can use a bowl over a pot of simmering water. Cook the mixture, whisking constantly and occasionally lifting the bowl to release the steam so it doesn’t get too hot. The mixture will thin out at first, then begin to thicken. The mixture will be ready when is has thickened and has more volume. It should take about 7-10 minutes and reach 160 degrees. Do not boil. When done, remove egg mixture from heat and set aside.
6. Place chocolate chips for mousse in a medium sized bowl and melt in the microwave in intervals of about 15-20 seconds, stirring between each interval, until smooth. You could also melt them in a double boiler, if you prefer.
7. Add the chocolate to the egg mixture and whisk until smooth. Set aside to cool to about room temperature.
8. In another bowl, make the whipped cream. Add the heavy whipping cream and powdered sugar to a large mixer bowl and whip until it reaches stiff peaks.
9. Fold about a ¼ cup of whipped cream into the chocolate mixture until combined. Then fold about a 1/4 of the chocolate mixture into the whipped cream. Slowly fold in the remaining chocolate mixture into the whipped cream.
10. Spread the chocolate mousse into an even layer on top of the brownie, then refrigerate until firm, 4-5 hours.
11. To finish off the cake, make the Baileys whipped cream. Add all ingredients to a large mixer bowl and whip on high speed until stiff peaks form.
12. Pipe swirls of whipped cream onto each slice, then finish with chocolate shavings and mini chocolate chips, if desired. Refrigerate until ready to serve.